This video starts with a discussion of various balance laws. The balance of mass is discussed in continuum mechanics settings. The idea of mass is a primitive concept in continuum mechanics. An example of Newton’s law of gravity is shown here. We also discuss the use of the continuous mass density function in continuum mechanics. This function remains continuous even under severe deformations, as explained by solid and fluid bodies. The parametrization of the mass density function is discussed, and a homogeneous body in its reference configuration is defined.
The mass density can change with deformation in some other configuration. The relation between mass density in the reference state, i.e., the undeformed state, and the mass density in the deformed configuration is derived using the conservation of mass.
Nest, we discuss mass density in reference and current configurations. How does mass density changing with time gives rise to the idea of balance of mass? Mass is conserved in the process of density change during deformation, and assuming that there is no process of transport and reaction. We show how density can be traced back to the reference configuration using the Lagrangian description of motion for solid mechanics. The Eulerian equation will be derived for mass density change in fluids.
The derivation of the mass density change in an Eulerian configuration continues from the previous video, and the conservation of mass equation in the current configuration is derived. This equation represents the balance of mass or conservation of mass in fluids. The conservation form of the equation is shown. The equation representing the balance of mass for fluids is also called the continuity equation.